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Delay dynamics of a Cournot game with heterogeneous duopolies

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  • Matsumoto, Akio
  • Szidarovszky, Ferenc

Abstract

We construct a Cournot duopoly model in a continuous-time framework and consider its dynamic behavior when the firms are heterogeneous in determining their output decision: one firm has an information delay in the competitor’s output as well as an implementation delay in its own output while the other firm does not have any delays. Two main results are obtained. One is that the information delay does not affect dynamics of the commodities and the other is that the implementation delay can destabilize the otherwise stable equilibrium. Furthermore, it is numerically confirmed that the two delay duopoly model can generate a wide spectrum of dynamics ranging from cyclic dynamics to chaos.

Suggested Citation

  • Matsumoto, Akio & Szidarovszky, Ferenc, 2015. "Delay dynamics of a Cournot game with heterogeneous duopolies," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 699-713.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:699-713
    DOI: 10.1016/j.amc.2015.07.051
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    References listed on IDEAS

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    1. Arnold B. Larson, 1964. "The Hog Cycle as Harmonic Motion," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 46(2), pages 375-386.
    2. Akio Matsumoto & Ferenc Szidarovszky, 2014. "Discrete-time delay dynamics of boundedly rational monopoly," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(1), pages 53-79, April.
    3. Howroyd, T. D. & Russell, A. M., 1984. "Cournot oligopoly models with time delays," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 97-103, October.
    4. Mackey, Michael C., 1989. "Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors," Journal of Economic Theory, Elsevier, vol. 48(2), pages 497-509, August.
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    Cited by:

    1. Culda, Loredana Camelia & Kaslik, Eva & Neamţu, Mihaela, 2022. "Stability and bifurcations in a general Cournot duopoly model with distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Fander, Atieh & Yaghoubi, Saeed, 2024. "Dynamic delay-based game approach in car and petrol supply chains under government intervention," Applied Energy, Elsevier, vol. 376(PA).
    3. Culda, Loredana Camelia & Kaslik, Eva & Neamţu, Mihaela & Sîrghi, Nicoleta, 2024. "Dynamics of a discrete-time mixed oligopoly Cournot-type model with three time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 524-539.

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